Consider a closed economy to which the Keynesian-cross analysis applies. Consump

Question

Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given by the equation C = 200 + 2/3(Y ? T). Planned investment is 300, as are government spending and taxes.

a. If Y is 1500, what is planned spending? What is inventory accumulation or decumulation? Should equilibrium Y be higher or lower than 1500? (Note: decumulation just means negative accumulation)

b. What is equilibrium Y? (Hint: Substitute the values of equations for planned consumption, investment, and government spending into the equation Y = C + I + G and then solve for Y.)

c. What is the multiplier for government spending?

Explanation / Answer

?Answer:-

?(a) Planned spending (AE) = C + I + G

AE = 200 + (2/3) (Y - 300) + 300 + 300

AE = 800 + (2/3) x (1,500)

AE = 800 + 1,000

AE = 1,800

Since Y < AE, there is inventory decumation and equilibrium Y should increase above $1,500.

?(b) In equilibrium, AE = Y

Y = 200 + (2/3) (Y - 300) + 300 + 300

Y = 800 + (2Y/3) - 200

[1 - (2/3)] x Y = 600

Y/3 = 600

Y = $1,800

?(c) Equilibrium consumption = 200 + (2/3) x (1,800 - 300) = 200 + (2/3) x 1,500 = 200 + 1,000 = $1,200

(d) When G = 200,

Y = 200 + (2/3) (Y - 300) + 300 + 200

Y = 700 + (2Y/3) - 200

[1 - (2/3)] x Y = 500

Y/3 = 500

Y = $1,500

Decrease in Y = $1,800 - $1,500 = $300

Multiplier = Decrease in Y / Decrease in G = $300 / $(300 - 200) = $300 / $100 = 3

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